Fix typos <noupdate>

src/fundamentals-of-ai-and-kr/module3/sections/_approx_inference.tex

@@ -113,7 +113,7 @@ The probability $\mathcal{S}$ of sampling a specific event $\matr{Z}$ and eviden
 probability of the single events in $\matr{Z}$ knowing their parents:
 \[ \mathcal{S}(\matr{Z}, \matr{E}) = \prod_{z_i \in \matr{Z}} \prob{z_i | \texttt{parents}(z_i)} \]
 
-The weights of a sample $(\matr{Z}, \matr{E})$ is given by the
+The weight of a sample $(\matr{Z}, \matr{E})$ is given by the
 probability of the single events in $\matr{E}$ knowing their parents:
 \[ \text{w}(\matr{Z}, \matr{E}) = \prod_{e_i \in \matr{E}} \prob{e_i | \texttt{parents}(e_i)} \]
 
@@ -129,7 +129,7 @@ probability of the single events in $\matr{E}$ knowing their parents:
                 &= \prob{\matr{Z}, \matr{E}}
             \end{split}
         \]
-        This is consequence of the global semantics of Bayesian networks.
+        This is a consequence of the global semantics of Bayesian networks.
     \end{proof}
 \end{theorem}
 
@@ -148,7 +148,7 @@ probability of the single events in $\matr{E}$ knowing their parents:
     \[ \langle C=\texttt{true}, S=\texttt{true}, \prob{R | C=\texttt{true}}, W=\texttt{false} \rangle \]
     \[ \langle C=\texttt{true}, S=\texttt{true}, R=\texttt{true}, W=\texttt{false} \rangle \]
 
-    The weight associated to the sample is given by the probabilities of the evidence:
+    The weight associated to the sample is given by the probability of the evidence:
     \[ 
         \begin{split}
             \text{w} &= \prob{S=\texttt{true} | C=\texttt{true}} \cdot \prob{W=\texttt{false} | S=\texttt{true}, R=\texttt{true}} \\

src/fundamentals-of-ai-and-kr/module3/sections/_bayesian_net.tex

@@ -158,7 +158,7 @@
 
         \begin{theorem}
             Two d-separated nodes are independent.
-            In other words, two nodes are independent if there is no active trail between them.
+            In other words, two nodes are independent if there are no active trails between them.
         \end{theorem}
 
     \item[Independence algorithm] \phantom{}
@@ -226,7 +226,7 @@
         
     
     \item[Markov blanket]
-        Each node is conditionally independent of all other nodes 
+        Each node is conditionally independent of all the other nodes 
         if its Markov blanket (parents, children, children's parents) is in the evidence.
         \begin{figure}[h]
             \centering

src/fundamentals-of-ai-and-kr/module3/sections/_exact_inference.tex

@@ -115,5 +115,4 @@ A variable $X$ is irrelevant if summing over it results in a probability of $1$.
 \marginnote{Clustering algorithm}
 
 Method that joins individual nodes to form clusters.
-Allows to estimate the posterior probabilities for $n$ variables with complexity $O(n)$ 
-(in contrast, variable elimination is $O(n^2)$).
+Allows to estimate the posterior probabilities for $n$ variables with complexity $O(n)$.

src/fundamentals-of-ai-and-kr/module3/sections/_intro.tex

@@ -22,9 +22,9 @@
 
 \subsection{Handling uncertainty}
 \begin{descriptionlist}
-    \item[Default/nonmonotonic logic] \marginnote{Default/nonmonotonic logic}
+    \item[Default/non-monotonic logic] \marginnote{Default/non-monotonic logic}
         Works on assumptions.
-        An assumption can be contradicted by an evidence.
+        An assumption can be contradicted by the evidence.
 
     \item[Rule-based systems with fudge factors] \marginnote{Rule-based systems with fudge factors}
         Formulated as premise $\rightarrow_\text{prob.}$ effect.